How would you solve this equation?

Question

The function is f(x)=2|x+1|-3 . What are the x-values when f(x)=3?

Answer 1

Assuming f(x)= 3, we get 3= 2|x+1| -3.

If we go ahead and rearrange it we get:

3= |x+1|. Now, suppose x≥-1 (i.e, it's to the right of -1 on the number line), then |x+1| = x+1 (because it's non-negative). So solving, we get x=2.

Now, supposing x<-1, we get |x+1| = -(x+1). So 3 = -(x+1), solving, we get x=-4.

So your solution set is going to be {-4,2}.